It said May now faces "the spectre of a leadership challenge", but it was "possible that after a period of resignations and political blood-letting, the Conservative Party will fall behind the prime minister".
The Brexit talks are being closely followed by the Indian government and more than 800 Indian companies based in the United Kingdom with annual revenues of almost £50 billion.
Tories unhappy with the current Brexit plans need to accept the "harsh truth" that there's no other option, William Hague has said.
May promised to deliver a "hard" Brexit when she came to power, but has since dialed back those aspirations following a loss of her Commons majority in last year's snap elections.
The Prime Minister is facing intense pressure to change course after a series of resignations - with two party chiefs following Boris Johnson and David Davis out of the door.
He said: "When it comes to a vote sometime around the end of this year, let us say that Theresa May has done a deal that bears some resemblance to what was put forward at Chequers with the EU". Gauke asked. "The challenge is (that it is) all very well for people to say "I wouldn't do this".
May's supporters are now reported to be anxious that more ministers could go and a no-confidence vote could be triggered.
Other amendments would force Britain to have a separate Value-Added Tax regime from the EU and ensure the Prime Minister has to table primary legislation if she wishes to keep Britain in the customs union.
The two resignations have left May badly exposed and raised questions over whether she will stand firm in her commitment to pursuing a "business-friendly" Brexit, or will be faced with more resignations and calls to quit herself. Speaking as he signed a joint EU-NATO declaration with NATO Secretary-General Jens Stoltenberg, Tusk was apparently alluding to Trump's upcoming meeting with Vladimir Putin when he said "it is always worth knowing who is your strategic friend and who is your strategic problem". "That dream is dying, suffocated by needless self-doubt".
Johnson said in his letter that May's plan to keep close economic ties with the bloc means Britain is heading for a "semi Brexit" that would leave Britain with the "status of a colony" of the EU.
Kit Malthouse is the new Housing Minister, replacing Dominic Raab.
The Sun, Britain's top-selling newspaper, which has long argued for Brexit, said May had made "blunder after blunder". He said Britain was heading for a "semi-Brexit".
"Michel Barnier and his taskforce can not negotiate an outcome that compromises the integrity of the single market for everybody else".
But it soon began to unravel when Davis resigned late on Sunday and launched a no-holds-barred attack on her plan, calling it "dangerous" and one which would give "too much away, too easily" to European Union negotiators, who would simply ask for more. "If people don't like this proposal, what is their alternative?"